**Abstract**

We present a new approach for designing a compact microring resonator structure based on only one multimode waveguide, which can provide a very high free spectral range (FSR) and capability of controlling the critical coupling. The silicon on insulator (SOI) waveguide and graphene-silicon waveguide (GSW) are used for the proposed structure. By changing the applied voltage on the graphene sheet, we can achieve a full control of the critical coupling. Some important properties of the proposed microring resonator such as free spectral range and quality factor are analyzed. We show that our structure can provide all characteristics of a single microring resonator with universal applications such as optical switching, modulating, filtering and signal processing, etc.

**Keywords:** multimode interference (MMI), silicon on insulator, multimode waveguide, directional coupler, finite difference time difference (FDTD), finite difference method (FDM), microring resonators (MRRs), graphene
